# Chaos, Strange Attractors, and Fractal Basin Boundaries in Nonlinear Dynamics

@article{Grebogi1987ChaosSA,
title={Chaos, Strange Attractors, and Fractal Basin Boundaries in Nonlinear Dynamics},
author={Celso Grebogi and Edward Ott and James A. Yorke},
journal={Science},
year={1987},
volume={238},
pages={632 - 638}
}
• Published 30 October 1987
• Physics
• Science
Recently research has shown that many simple nonlinear deterministic systems can behave in an apparently unpredictable and chaotic manner. This realization has broad implications for many fields of science. Basic developments in the field of chaotic dynamics of dissipative systems are reviewed in this article. Topics covered include strange attractors, how chaos comes about with variation of a system parameter, universality, fractal basin boundaries and their effect on predictability, and…
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## References

SHOWING 1-10 OF 68 REFERENCES
Noise and chaos in a fractal basin boundary regime of a Josephson junction.
• Physics
Physical review letters
• 1985
It is shown that if enough noise is present to push the orbits into the basin boundary, behavior similar to intrinsic chaos results.
Fractal Basin Boundaries, Long-Lived Chaotic Transients, And Unstable-Unstable Pair Bifurcation
• Physics
• 1983
A new type of bifurcation to chaos is pointed out and discussed. In this bifurcation two unstable fixed points or periodic orbits are created simultaneously with a strange attractor which has a
Metastable chaos: The transition to sustained chaotic behavior in the Lorenz model
• Physics
• 1979
The system of equations introduced by Lorenz to model turbulent convective flow is studied here for Rayleigh numbersr somewhat smaller than the critical value required for sustained chaotic behavior.
Fractal basin boundaries and homoclinic orbits for periodic motion in a two-well potential.
• Moon, Li
• Physics
Physical review letters
• 1985
A fractal-looking basin boundary for forced periodic motions of a particle in a two-well potential is observed in numerical simulation and raises questions about predictability in nonchaotic dynamics of nonlinear systems.
Metamorphoses of basin boundaries in nonlinear dynamical systems.
A basin boundary can undergo sudden changes in its character as a system parameter passes through certain critical values. In particular, basin boundaries can suddenly jump in position and can change
Dimension of Strange Attractors
• Mathematics, Physics
• 1980
A relationship between the Lyapunov numbers of a map with a strange attractor and the dimension of the strange attractor has recently been conjectured. Here, the conjecture is numerically tested with
Laser chaotic attractors in crisis.
• Physics
Physical review letters
• 1986
Different crises, i.e., abrupt qualitative changes in the properties of attractors, have been observed in a C${\mathrm{O}}_{2}$ laser with internal modulation. They are shown to be related to
Intermittent transient chaos at interior crises in the diode resonator
• Physics
• 1984
We report experimental measurements and calculations using a model on a driven, dissipative, dynamical system which shows chaotic behavior. The system is the diode resonator composed of the series
Simple mathematical models with very complicated dynamics
This is an interpretive review of first-order difference equations, which can exhibit a surprising array of dynamical behaviour, from stable points, to a bifurcating hierarchy of stable cycles, to apparently random fluctuations.